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The elementary theory of the Frobenius automorphisms
, 2004
"... We lay down some elements of a geometry based on difference equations. Various constructions of algebraic geometry are shown to have meaningful analogs: dimensions, blowingup, moving lemmas. Analogy aside, the geometry of difference equations has two quite different functorial connections with ordin ..."
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Cited by 48 (0 self)
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of discrete valuation rings. The central application and motivation is the determination of the elementary theory of the class of Frobenius difference fields (algebraically closed fields of characteristic p> 0,
Characterizing automorphism and . . .
, 2011
"... Permutation polytopes are polytopes whose vertices are determined by a representation of a permutation group, such as the cyclic group on n elements or the dihedral group on n elements. These polytopes appear in many different applications, yet little research has been done on any save the Birkhof ..."
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in t which counts the number of integer points contained within the t th dilation of the polytope. We also consider the polytopes associated to the automorphism groups of trees and rigid graphs. Our results include Ehrhart polynomials and volumes of the polytopes corresponding to cyclic and dihedral groups
Automorphisms and Encoding of AG and Order Domain Codes
, 2007
"... We survey some encoding methods for AG codes, focusing primarily on one approach utilizing code automorphisms. If a linear code C over Fq has a finite abelian group H as a group of automorphisms, then C has the structure of a module over a polynomial ring P. This structure can be used to develop sys ..."
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Cited by 4 (0 self)
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We survey some encoding methods for AG codes, focusing primarily on one approach utilizing code automorphisms. If a linear code C over Fq has a finite abelian group H as a group of automorphisms, then C has the structure of a module over a polynomial ring P. This structure can be used to develop
Finite quasiFrobenius modules and linear codes
 J. Algebra Appl
"... The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasiFrobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper we subsume these results by studying linear codes over q ..."
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Cited by 16 (4 self)
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The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasiFrobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper we subsume these results by studying linear codes over
On cyclic convolutional codes
 Acta Applicandae Mathematicae
"... We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [19, 22]. Codes of this type are described as submodules of F[z]n with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result of ..."
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Cited by 15 (7 self)
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We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [19, 22]. Codes of this type are described as submodules of F[z]n with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result
FIELDS OF INVARIANTS OF FINITE LINEAR GROUPS
, 707
"... Let G be a finite group of order n and let k be a field. Consider a rational (i.e., pure transcendental) extension K/k of transcendence degree n. We may assume that K = k({xg}), where g runs through all the elements of G. The group G naturally acts on K via h(xg) = xhg. E. Noether [Noe13] ..."
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Let G be a finite group of order n and let k be a field. Consider a rational (i.e., pure transcendental) extension K/k of transcendence degree n. We may assume that K = k({xg}), where g runs through all the elements of G. The group G naturally acts on K via h(xg) = xhg. E. Noether [Noe13]
Linear codes over finite chain rings
 ELECTRONIC JOURNAL OF COMBINATORICS
, 1998
"... The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a wellknown result for linear codes over fields, we prove that there exists a onetoone correspondence between socalled fat linear codes over chain rings and multisets of ..."
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Cited by 6 (0 self)
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The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a wellknown result for linear codes over fields, we prove that there exists a onetoone correspondence between socalled fat linear codes over chain rings and multisets
Results 11  20
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2,582